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## Re: How to average to find 'circular' symmetry in a SQUARE matrix?

 From: Robert A. Macy Subject: Re: How to average to find 'circular' symmetry in a SQUARE matrix? Date: Mon, 15 Jan 2007 17:31:51 -0800

```Doug,

Yes, 1 degree, 10 degrees, or 127 degrees, image that is
represented by x-y data set is perfectly axisymmetric.

How do I use polar notation to average?

- Robert -

Chris,

How do I use 2D Lagrange interpolation?  Sounds exactly
what I need, but didn't find any functions that looked like
it would do that.

What were you using it on?

- Robert -

> Maybe I misunderstand, but it sounds like
> you need to do interpolation in 2D.
>
> There is a 2D form of Lagrange interpolation
> that is perhaps the easiest thing.
>
> The idea is to interpolate over a desired circle
> (appropriately centered), and average the interpolants.
>
> I actually had this problem in processing some
> grey-scale images from a thin-film optics experiment.
>
> Chris Z

On Mon, 15 Jan 2007 19:06:24 -0500
> Hi Robert
>
>  Do you mean by rotational symmetry  that if you rotate
> it 10 deg ( or
> 20 or 30 etc.) it still has symmetry or do you mean
> rotate by 90 deg. steps.
>
>
> If it is by any deg. then maybe you could use polar
> notation?
>
> Doug Stewart

```